Finite Group Databasebeta

← #14478522

Subgroups — #14478522

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756528C211yesmaximal, characteristic, complemented
2#11753983C211yesmaximal, characteristic, complemented
3C5×#5193C211yesmaximal, characteristic, complemented
4C3×#65483C211yesmaximal, characteristic, complemented
5#11748310C212yesmaximal, complemented
6#11748293C212yesmaximal, complemented
7#11748287C212yesmaximal, complemented
8#11748268C212yesmaximal, complemented
9C2×#90939C211yesmaximal, characteristic, complemented
10#11747544C211yesmaximal, characteristic, complemented
11#11747531C211yesmaximal, characteristic, complemented
12#10613767—31nomaximal, Hall
13#92100—21no—
14#92018—21no—
15C3×C5×#135C2211yescharacteristic, complemented
16#91838—21no—
17#91808C2212yescomplemented
18#91803—22no—
19D8×D15C2212yescomplemented
20C2×D120C2211yescharacteristic, complemented
21#91790C2211yescharacteristic
22C2×C5×D24C2211yescharacteristic, complemented
23C3×#4050C2211yescharacteristic, complemented
24#91299—21no—
25#91279C2212yescomplemented
26#91257—22no—
27#91256C2212yescomplemented
28C5×#828C2212yescomplemented
29C5×#826C2212yescomplemented
30C5×#812C2211yescharacteristic, complemented
31C3×#3961C2211yescharacteristic, complemented
32C3×#3960C2211yescharacteristic, complemented
33C3×#3959C2211yescharacteristic, complemented
34C3×#3958C2211yescharacteristic, complemented
35C2×C3×#672C2211yescharacteristic, complemented
36#90943C2212yescomplemented
37#90939C2212yescomplemented
38#90939C2212yescomplemented
39#90938C2212yescomplemented
40#90936C2212yescomplemented
41#90933C2212yescomplemented
42#82031—51nomaximal, Hall
43#66103—31no—
44#66091—31no—
45C5×#509—31no—
46#65483D311yescharacteristic, complemented
47C2×#3958—31no—
48#65205—32no—
49#65203—32no—
50#65200—32no—
51D5×D16—32no—
52#65197—31no—
53#65196—31no—
54C3×C5×#41—21no—
55#6821—22no—
56D4×D15—22no—
57D4×D15—42no—
58#6817—41no—
59#6817D411yescharacteristic
60C2×D60—21no—
61C2×D60—41no—
62C2×C5×D12—21no—
63C3×#709—21no—
64D3×C22⋊D5—42no—
65#6777—22no—
66D5×D12—41no—
67#6772—41no—
68#6768—22no—
69C3×C5×Q16C2311yescharacteristic
70C3×C5×SD16—21no—
71C3×C5×D8C2311yescharacteristic
72C2×C3×C5×C8C2311yescharacteristic
73#6717—22no—
74#6715—22no—
75#6710D411yescharacteristic
76D120—21no—
77D120C2312yes—
78#6705D412yes—
79C8×D15C2312yes—
80C5×D24—21no—
81C5×D24C2312yes—
82C3×Dic20C2311yescharacteristic
83C3×D40C2311yescharacteristic
84C3×#677—21no—
85#6656—22no—
86#6652—22no—
87C3×#672C2311yescharacteristic
88C3×#672C2311yescharacteristic
89C5×C3⋊C16C2312yes—
90#5769—51no—
91#5769—51no—
92C3×#508—51no—
93#5193—51no—
94#5193D511yescharacteristic, complemented
95#4919—52no—
96#4914—52no—
97#4914—52no—
98D3×D16—52no—
99C2×D48—51no—
100#4901—51no—
101#4149—61no—
102#4144—61no—
103C5×#135C2×D311yescharacteristic, complemented
104C2×C5×D8—31no—
105#4095—61no—
106#4078—61no—
107#4065—32no—
108#4060—62no—
109#4058—32no—
110#4057—62no—
111D5×D8—32no—
112D5×D8—32no—
113#4050C2×D311yescharacteristic, complemented
114C2×D40—31no—
115#4047—31no—
116C5×SD32—32no—
117C5×D16—32no—
118C5×M32—31no—
119#3961C2×D311yescharacteristic, complemented
120#3960C2×D311yescharacteristic, complemented
121#3959C2×D311yescharacteristic, complemented
122#3958—32no—
123#3958—32no—
124#3958C2×D311yescharacteristic, complemented
125C2×#672C2×D311yescharacteristic, complemented
126#3932—32no—
127D80—32no—
128#3930—32no—
129D5×C16—32no—
130#3415—151noSylow
131C22×D15—41no—
132C22×D15—42no—
133C22×C5×D3—41no—
134C2×D3×D5—42no—
135C3×C5×Q8—21no—
136C3×C5×D4—21no—
137C3×C5×D4—41no—
138C2×C3×C4×C5—41no—
139C2×C3×C4×C5C2×D411yescharacteristic
140#1220—42no—
141#1220D812yes—
142D60—22no—
143D60—42no—
144D60—41no—
145D60D811yescharacteristic
146C4×D15—42no—
147C4×D15C2×D412yes—
148Dic30D811yescharacteristic
149C5×D12—22no—
150C5×D12—41no—
151C3×C22⋊D5—41no—
152C3×D20—21no—
153C3×C4×D5—41no—
154C3×Dic10—21no—
155#1203—42no—
156#1201—42no—
157D3×Dic5—42no—
158C3×C5×C8C2×D411yescharacteristic
159C3×C5×C8C2411yescharacteristic
160C3⋊#168C2×D412yes—
161#1009—101no—
162#1009—101no—
163C3×#135—51no—
164C3×#135C2×D511yescharacteristic, complemented
165#949—101no—
166#949—101no—
167#919—52no—
168#919—52no—
169#914—102no—
170#914—102no—
171D3×D8—52no—
172D3×D8—52no—
173C2×D24—51no—
174C2×D24C2×D511yescharacteristic, complemented
175#901—51no—
176C3×Q32—51no—
177C3×SD32—51no—
178C3×SD32—51no—
179C3×D16—51no—
180C2×C3×C16—51no—
181#828—52no—
182#828C2×D512yescomplemented
183#826—52no—
184#826C2×D512yescomplemented
185#812C2×D511yescharacteristic, complemented
186D48—52no—
187D48—52no—
188#798—52no—
189D3×C16—52no—
190C5×#41—21no—
191C2×C5×D4—61no—
192C2×C22⋊D5—122no—
193#713—62no—
194#711—62no—
195#711—121no—
196D4×D5—62no—
197D4×D5—62no—
198D4×D5—121no—
199D4×D5—122no—
200#709—21no—
201#709—31no—
202#709—121no—
203C2×D20—61no—
204C2×D20—121no—
205C5×Q16C22×D311yescharacteristic
206C5×SD16—21no—
207C5×D8—32no—
208C5×D8—61no—
209C5×D8C22×D311yescharacteristic
210C2×C5×C8C22×D311yescharacteristic
211#688—62no—
212#687—62no—
213#686—62no—
214#686—62no—
215#681—31no—
216Dic20C22×D311yescharacteristic
217D40—32no—
218D40—61no—
219D40C22×D311yescharacteristic
220#677—21no—
221#676—32no—
222C8×D5—32no—
223C5×C16—32no—
224#672C22×D311yescharacteristic
225#672C22×D311yescharacteristic
226#576—151no—
227#576—151no—
228#509—31no—
229#509—151no—
230#509—152no—
231#509—152no—
232#508—51no—
233#508—152no—
234C2×D16—151no—
235C2×D16—152no—
236#504—151no—
237C22×C3×C5—41no—
238C22×C3×C5C2×D811yescharacteristic
239C2×D15—42no—
240C2×D15—162no—
241C2×D15—161no—
242C2×D15C2×D812yes—
243C2×C5×D3—42no—
244C2×C5×D3—161no—
245C2×C3×D5—41no—
246D3×D5—162no—
247C3×C4×C5—41no—
248C3×C4×C5C2×D811yescharacteristic
249C3×C4×C5C22×D411yescharacteristic
250Dic15C2×D812yes—
251C3×Dic5—41no—
252C3×#41—21no—
253C3×#41—101no—
254#239—102no—
255#239—102no—
256D3×D4—102no—
257D3×D4—102no—
258D3×D4—202no—
259D3×D4—202no—
260#235—51no—
261#235—201no—
262#235—201no—
263C2×D12—21no—
264C2×D12—101no—
265C2×D12—201no—
266C2×D12—201no—
267C3×Q16—51no—
268C3×Q16C22×D511yescharacteristic
269C3×SD16—21no—
270C3×SD16—101no—
271C3×D8—51no—
272C3×D8C22×D511yescharacteristic
273C2×C3×C8C22×D511yescharacteristic
274#215—102no—
275#215—102no—
276#213—102no—
277#213—102no—
278#208—51no—
279D24—21no—
280D24—52no—
281D24—101no—
282D24C22×D512yes—
283ΓL(1,𝔽25)—52no—
284D3×C8—52no—
285C3×C16—51no—
286C3×C16—51no—
287C3⋊C16C22×D512yes—
288C23×C5—121no—
289C22×D5—122no—
290C22×D5—122no—
291C22×D5—121no—
292C5×Q8—21no—
293C5×D4—21no—
294C5×D4—41no—
295C5×D4—62no—
296C5×D4—121no—
297C2×C4×C5—41no—
298C2×C4×C5D3×D411yescharacteristic
299C22⋊D5—32no—
300C22⋊D5—41no—
301C22⋊D5—122no—
302C22⋊D5—122no—
303C22⋊D5—122no—
304C2×Dic5—122no—
305D20—21no—
306D20—31no—
307D20—62no—
308D20—122no—
309D20—121no—
310C4×D5—32no—
311C4×D5—41no—
312C4×D5—122no—
313Dic10—21no—
314Dic10—31no—
315C5×C8D3×D411yescharacteristic
316C5×C8C23×D311yescharacteristic
317#168—32no—
318H(5,𝔽2)—301no—
319H(5,𝔽2)—301no—
320AGL(1,ℤ/8)—302no—
321AGL(1,ℤ/8)—302no—
322AGL(1,ℤ/8)—301no—
323AGL(1,ℤ/8)—301no—
324#135—51no—
325#135—152no—
326#135—152no—
327#135D3×D511yescharacteristic, complemented
328C2×D8—31no—
329C2×D8—152no—
330C2×D8—152no—
331C2×D8—151no—
332#131—151no—
333Q32—51no—
334SD32—32no—
335SD32—51no—
336SD32—51no—
337SD32—152no—
338D16—32no—
339D16—51no—
340D16—152no—
341D16—152no—
342D16—152no—
343M32—31no—
344M32—152no—
345C2×C16—51no—
346C2×C16—152no—
347C2×C3×C5—21no—
348C2×C3×C5—81no—
349C2×C3×C5C22×D811yescharacteristic
350D15—22no—
351D15—82no—
352C3×D5—81no—
353C5×D3—82no—
354C22×D3—41no—
355C22×D3—202no—
356C22×D3—202no—
357C22×D3—201no—
358C3×Q8—21no—
359C3×Q8—101no—
360C3×D4—21no—
361C3×D4—41no—
362C3×D4—101no—
363C3×D4—201no—
364C2×C3×C4—41no—
365C2×C3×C4—201no—
366C2×C3×C4D4×D511yescharacteristic
367#67—52no—
368#67—202no—
369#67—202no—
370D12—22no—
371D12—41no—
372D12—51no—
373D12—102no—
374D12—202no—
375D12—202no—
376D12—201no—
377C4×D3—52no—
378C4×D3—202no—
379C4×D3—202no—
380Dic6—51no—
381C3×C8D4×D511yescharacteristic
382C3×C8C23×D511yescharacteristic
383C3⋊C8—52no—
384C22×C5—41no—
385C22×C5—122no—
386C22×C5—481no—
387C22×C5D3×D811yescharacteristic
388C2×D5—32no—
389C2×D5—41no—
390C2×D5—122no—
391C2×D5—482no—
392C2×D5—482no—
393C2×D5—481no—
394C4×C5—41no—
395C4×C5D3×D811yescharacteristic
396C4×C5C2×D3×D411yescharacteristic
397Dic5—32no—
398Dic5—41no—
399#41—21no—
400#41—101no—
401#41—151no—
402#41—302no—
403#41—302no—
404#41—601no—
405#41—601no—
406C2×D4—61no—
407C2×D4—302no—
408C2×D4—302no—
409C2×D4—301no—
410C2×D4—601no—
411C2×D4—601no—
412C2×D4—602no—
413C2×D4—602no—
414Q16—51no—
415Q16C2×D3×D511yescharacteristic
416SD16—21no—
417SD16—101no—
418SD16—302no—
419SD16—302no—
420D8—32no—
421D8—51no—
422D8—61no—
423D8—152no—
424D8—302no—
425D8—302no—
426D8—301no—
427D8C2×D3×D511yescharacteristic
428M16—151no—
429M16—152no—
430C2×C8—152no—
431C2×C8C2×D3×D511yescharacteristic
432C16—32no—
433C16—51no—
434C16—51no—
435C3×C5#341511yescharacteristic, complemented, Hall
436C22×C3—41no—
437C22×C3—201no—
438C22×C3D5×D811yescharacteristic
439C2×D3—42no—
440C2×D3—52no—
441C2×D3—161no—
442C2×D3—202no—
443C2×D3—802no—
444C2×D3—802no—
445C2×D3—801no—
446C3×C4—41no—
447C3×C4—201no—
448C3×C4D5×D811yescharacteristic
449C3×C4C2×D4×D511yescharacteristic
450Dic3—52no—
451C2×C5—21no—
452C2×C5—81no—
453C2×C5—242no—
454C2×C5C2×D3×D811yescharacteristic
455D5—62no—
456D5—81no—
457D5—242no—
458C23—121no—
459C23—602no—
460C23—602no—
461C23—601no—
462Q8—21no—
463Q8—101no—
464Q8—151no—
465D4—21no—
466D4—41no—
467D4—62no—
468D4—101no—
469D4—121no—
470D4—152no—
471D4—151no—
472D4—201no—
473D4—302no—
474D4—602no—
475D4—602no—
476D4—602no—
477D4—602no—
478D4—601no—
479C2×C4—41no—
480C2×C4—152no—
481C2×C4—201no—
482C2×C4—602no—
483C2×C4—602no—
484C2×C4#679011yescharacteristic
485C8—152no—
486C8#679011yescharacteristic
487C8C22×D3×D511yescharacteristic
488C2×C3—21no—
489C2×C3—81no—
490C2×C3—401no—
491C2×C3C2×D5×D811yescharacteristic
492D3—82no—
493D3—102no—
494D3—402no—
495C5#8203111yescharacteristic, complemented, Sylow
496C22—41no—
497C22—122no—
498C22—152no—
499C22—201no—
500C22—481no—
501C22—602no—
502C22—2401no—
503C22—2402no—
504C22—2402no—
505C22#9148111yescharacteristic
506C4—41no—
507C4—152no—
508C4—201no—
509C4#9148111yescharacteristic
510C4C2×#679011yescharacteristic
511C3#1061376711yescharacteristic, complemented, Sylow
512C2—21no—
513C2—81no—
514C2—242no—
515C2—302no—
516C2—401no—
517C2—1202no—
518C2C2×#9148111yescharacteristic
subgroupG/H
centerC2C2×#91481
commutator, cosocleC3×C5×C8C24
FrattiniC8C22×D3×D5
FittingC3×C5×#135C22
socleC2×C3×C5C22×D8
hypercenter#135D3×D5
hypocenterC3×C5#3415
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #11756528C2semidirect
2. #11753983C2semidirect
3. C5×#5193C2semidirect
4. C3×#65483C2semidirect
5. #11748310C2semidirect
6. #11748293C2semidirect
7. #11748287C2semidirect
8. #11748268C2semidirect
9. C2×#90939C2semidirect
10. #11747544C2semidirect
11. #11747531C2semidirect
15. C3×C5×#135C22semidirect
17. #91808C22semidirect
19. D8×D15C22semidirect
20. C2×D120C22semidirect
22. C2×C5×D24C22semidirect
23. C3×#4050C22semidirect
25. #91279C22semidirect
27. #91256C22semidirect
28. C5×#828C22semidirect
29. C5×#826C22semidirect
30. C5×#812C22semidirect
31. C3×#3961C22semidirect
32. C3×#3960C22semidirect
33. C3×#3959C22semidirect
34. C3×#3958C22semidirect
35. C2×C3×#672C22semidirect
36. #90943C22semidirect
37. #90939C22semidirect
38. #90939C22semidirect
39. #90938C22semidirect
40. #90936C22semidirect
41. #90933C22semidirect
46. #65483D3semidirect
94. #5193D5semidirect
103. C5×#135C2×D3semidirect
113. #4050C2×D3semidirect
119. #3961C2×D3semidirect
120. #3960C2×D3semidirect
121. #3959C2×D3semidirect
124. #3958C2×D3semidirect
125. C2×#672C2×D3semidirect
164. C3×#135C2×D5semidirect
174. C2×D24C2×D5semidirect
182. #828C2×D5semidirect
184. #826C2×D5semidirect
185. #812C2×D5semidirect
327. #135D3×D5semidirect
435. C3×C5#3415semidirect
495. C5#82031semidirect
511. C3#10613767semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117565282
#117539832
C5×#51932
C3×#654832
#117483102
#117482932
#117482872
#117482682
C2×#909392
#117475442
#117475312
#106137673
#820315